docs: def friction_plate_Martin_1999(Re, plate_enlargement_factor):
      r'''Calculates Darcy friction factor for single-phase flow in a 
      Chevron-style plate heat exchanger according to [1]_. 
      
      .. math::
          \frac{1}{\sqrt{f_f}} = \frac{\cos \phi}{\sqrt{0.045\tan\phi
          + 0.09\sin\phi + f_0/\cos(\phi)}} + \frac{1-\cos\phi}{\sqrt{3.8f_1}}
          
      .. math::
          f_0 = 16/Re \text{ for } Re < 2000
          
      .. math::
          f_0 = (1.56\ln Re - 3)^{-2} \text{ for } Re \ge 2000
          
      .. math::
          f_1 = \frac{149}{Re} + 0.9625 \text{ for } Re < 2000
          
      .. math::
          f_1 = \frac{9.75}{Re^{0.289}} \text{ for } Re \ge 2000
          
      Parameters
      ----------
      Re : float
          Reynolds number with respect to the hydraulic diameter of the channels,
          [-]
      plate_enlargement_factor : float
          The extra surface area multiplier as compared to a flat plate
          caused the corrugations, [-]
  
      Returns
      -------
      fd : float
          Darcy friction factor [-]
  
      Notes
      -----
      Based on experimental data from Re from 200 - 10000 and enhancement 
      factors calculated with chevron angles of 0 to 80 degrees. See 
      `PlateExchanger` for further clarification on the definitions.
      
      The length the friction factor gets multiplied by is not the flow path
      length, but rather the straight path length from port to port as if there
      were no chevrons.
      
      Note there is a discontinuity at Re = 2000 for the transition from
      laminar to turbulent flow, although the literature suggests the transition
      is actually smooth.
      
      This was first developed in [2]_ and only minor modifications by the 
      original author were made before its republication in [1]_. 
      This formula is also suggested in [3]_
  
      Examples
      --------
      >>> friction_plate_Martin_1999(Re=20000, plate_enlargement_factor=1.15)
      2.284018089834134
  
      References
      ----------
      .. [1] Martin, Holger. "Economic optimization of compact heat exchangers."
         EF-Conference on Compact Heat Exchangers and Enhancement Technology for 
         the Process Industries, Banff, Canada, July 18-23, 1999, 1999. 
         https://publikationen.bibliothek.kit.edu/1000034866.
      .. [2] Martin, Holger. "A Theoretical Approach to Predict the Performance 
         of Chevron-Type Plate Heat Exchangers." Chemical Engineering and 
         Processing: Process Intensification 35, no. 4 (January 1, 1996): 301-10. 
         https://doi.org/10.1016/0255-2701(95)04129-X.
      .. [3] Shah, Ramesh K., and Dusan P. Sekulic. Fundamentals of Heat 
         Exchanger Design. 1st edition. Hoboken, NJ: Wiley, 2002.
      '''
      phi = plate_enlargement_factor
      
      if Re < 2000.:
          f0 = 16./Re
          f1 = 149./Re + 0.9625
      else:
          f0 = (1.56*log(Re) - 3.0)**-2
          f1 = 9.75*Re**-0.289
          
      rhs = cos(phi)*(0.045*tan(phi) + 0.09*sin(phi) + f0/cos(phi))**-0.5
      rhs += (1. - cos(phi))*(3.8*f1)**-0.5
      ff = rhs**-2.
      return ff*4.0